Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 - 16x}{x - 10} = \dfrac{3x - 90}{x - 10}$
Multiply both sides by $x - 10$ $ \dfrac{x^2 - 16x}{x - 10} (x - 10) = \dfrac{3x - 90}{x - 10} (x - 10)$ $ x^2 - 16x = 3x - 90$ Subtract $3x - 90$ from both sides: $ x^2 - 16x - (3x - 90) = 3x - 90 - (3x - 90)$ $ x^2 - 16x - 3x + 90 = 0$ $ x^2 - 19x + 90 = 0$ Factor the expression: $ (x - 9)(x - 10) = 0$ Therefore $x = 9$ or $x = 10$ However, the original expression is undefined when $x = 10$. Therefore, the only solution is $x = 9$.